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# FACETS: The Building Blocks of 3D Geometry

FACETS are a flexible construction toy based on the 3D geometry of the Archimedean solids. In the figure above, two rhombicosidodecahedrons (the small spheres in the two-tone brown FACETS) are nested into the geometric structure of the larger truncated icosidodecahedron (the large sphere made out of blonde FACETS).

# The origin of FACETS

Hello Kickstarter community. I’m Ron Worley and I've created a marvelous toy that I want to share with the you. They are called FACETS, like the faces of a gemstone.

When I was a kid (and still today) I loved to build things: wooden blocks, Lincoln logs, tinker toys, erector set. For me, building things was the best kind of play. I was especially impressed with 3D geometry and spent many hours building cardboard models of the Platonic and Archimedean solids. Combine the fun of building things with the fun of playing with magnets and FACETS embody three of my most favorite things in the world: geometry, magnets and play. FACETS are a toy that I would have loved to have when I was a kid, I just had to wait until I could make them for myself.

The original prototype for FACETS was a hexagonal shaped block (like the yellow faces below) based on the geometry of the icosahedron. With the original Icosa-FACETS, 20 blocks connected in the same orientation form a truncated icosahedron.

I made the original Icosa-FACETS as a construction toy/puzzle for Alice, my 5-year old granddaughter. She was able to assemble the FACETS into an icosahedron without too much difficulty.

The current model of FACETS is based on the geometry of the truncated tetrahedron.

# FACETS: What they do

I designed FACETS to be a fun and fascinating construction toy for children and I have conducted numerous informal studies, tests, and evaluations of how FACETS are received by kids and their elders. This has generally been in the form of friends and acquaintances and their children who have come to our home over the past two years, but FACETS have been to "show and tell" and to the playground of a local elementary school where they were well received and were quite the center of attention. Magnets can do that.

The initial introduction to FACETS is pretty consistent for both young and old. There is a short period of critical evaluation: "these things look really interesting, but what do they do?" Then the pieces begin to snap together, this way and that, and hey!, you've got yourself a ring. And then another ring connected to the first, but turned in the other direction like the links in a chain. Then the structures begin to grow and spread out, and fall over. After a while the rings and loops are connected together in larger and larger structures that interlink and hold together. And, not surprisingly, the more balanced and symmetrical the constellation of FACETS the more stable and the larger it is able to grow.

FACETS are truly captivating. They grab your attention. FACETS are a highly flexible and yet very simple reward based hand-eye manipulation of pieces that teaches stability, symmetry and balance. Excellent for the development of manual dexterity! The reward is immediate: the pieces snap together in rings and links and chains! And the rewards are progressive as the structures and connections of structures grow larger and larger. Careful! Playing with FACETS can be addictive! By analogy, playing with FACETS is like playing that video game where the game pieces spin and flip and fit together, except that instead of playing a game on a screen, you are using your hands to build 3D structures with geometrically shaped blocks that snap together magnetically. The geometry of FACETS is the reason they work, but not what they do.

A big part of the attraction of FACETS is the magnetic action. The magnets cause the FACETS to snap together and stick, but the connections are easily broken and the pieces can be flipped over and snapped together in the opposite orientation. The variety of different structures that can be created is endless.

I designed FACETS to be an engaging and entertaining construction toy for children, but they do much more. FACETS are ideal for anyone who wants to stimulate their sensitivity to 3D geometry (3D geeks) or for anyone who just likes to build stuff. I have been admonished many times for the late night "snap, snap, snap" of FACETS as numerous models, designs and geometric structures were built and grew, collapsed and were reconfigured on the fly. FACETS have provided me with uncountable hours of creative fun.

# FACETS: How they work

FACETS are rectangular wooden blocks that have small magnets embedded around the edges of the block. The magnets cause the blocks to snap together and adhere so long as the blocks are brought together in the proper orientation.

The edges of the blocks are beveled at the proper angle so that six FACETS brought together side by side in the proper orientation will snap together to form a hexagonal prism.

The ends of the blocks are beveled in the opposite direction so that five FACETS brought together end to end in the proper orientation will snap together to form a pentagonal prism.

The hexagonal prisms interlock back to back and at right angles to the pentagonal prisms (like the links in a chain) in the assembly and construction of ever larger and more complex geometric structures.

These FACETS are called HexTetra FACETS because when four hexagonal prisms are brought together end to end, the inner surface of the resulting structure is a truncated tetrahedron.

FACETS are an engaging construction toy that is ideal for anyone who loves to build things. Simple enough to entertain a 5-year old, complex enough to engage a mathematician. FACETS are intended for ages 5 and up, but will provide hours of fun and fiddling for anyone who likes to tinker.

There has been some negative publicity recently about the dangers that are posed by small super strong magnets in the hands of children. I have devoted considerable attention to make sure that FACETS are a proper size to avoid any choking hazard and that the magnets used in FACETS are permanently embedded in the wooden pieces. I hope to see FACETS in the hands of inquisitive children everywhere and will make certain that they undergo thorough product safety testing before FACETS hit the shelves.

# REWARDS

As with any construction toy, the more pieces you have the more intricate and elaborate the structures you can build. Many interesting structures and models can be created with the FACETS included in the smaller sets, but the truly spectacular geometric structures that can be created with FACETS require greater and greater numbers of pieces. Fortunately, the sets can be combined to create an ever growing collection of FACETS.

**Pledge Level 1: The Tetrahedron**

For a pledge of $25.00 USD you will receive the basic set of 24 FACETS. This is the number of FACETS needed to construct a truncated tetrahedron, the defining geometric structure for this model of FACETS.

The Tetrahedron set of FACETS is not large, but there are numerous interesting structures and models that can be constructed with the basic set. This is the proper size set of FACETS for hand-held lap-top structure morphing for child size hands. Below are examples of some models constructed with the 24 FACETS in the Tetrahedron set.

**Pledge Level 2: The Double Tetrahedron**

For a pledge of $50.00 USD you will receive a set of 48 FACETS. This is the number of FACETS needed to construct an interlinked double tetrahedron.

This is the proper size set of FACETS for hand-held lap-top structure morphing for adult size hands. Below are examples of some models constructed with the 48 FACETS of the Double Tetrahedron set.

**Pledge Level 3: The Tetra Pyramid**

For a pledge of $100.00 USD you will receive a set of 96 FACETS. This is the number of FACETS needed to construct a two-frequency tetrahedral pyramid (a tetrahedron of tetrahedrons). The Tetra Pyramid can be displayed in its geometric structure as a three sided pyramid,

or in its atomic structure like the tetrahedrally bonded carbon atoms in the crystal structure of a diamond.

The Tetra Pyramid set includes enough FACETS to construct the small sphere known as the rhombicosidodecahedron.

This set of FACETS is perfect for table top and desk top assembly and construction of models and geometric structures. Below are examples of some models constructed with the 96 FACETS of the Tetra Pyramid set.

**Pledge Level 4: The Great Sphere**

For a pledge of $200.00 USD you will receive a deluxe set of 210 FACETS. This is the number of FACETS needed to construct the large sphere known as the truncated icosidodecahedron.

This set of FACETS is ideal for the table top exploration and discovery of the interlinked geometric structures of the Archimedean solids. Below are examples of some models constructed with the 210 FACETS in the Great Sphere set.

**Pledge Level 5: The Geodesic Sphere**

For a pledge of $350.00 USD you will receive a super deluxe set of 360 FACETS. This is the number of FACETS needed to construct the enormous Geodesic Sphere. This is a sphere that is composed of six interlinked, overlapping and symmetrically distributed geodesics (great circles) of the sphere.

Below is an example of a tower constructed with the 360 FACETS in the Geodesic Sphere set.

**Pledge Level 6: The Dodecahydroid**

For a pledge of $500.00 USD you will receive the ultimate set of 570 FACETS. This is the number of FACETS in the Great Sphere and the Geodesic Sphere combined! This is the number of FACETS needed to construct the truly incomparable Dodecahydroid. This is a geometric structure that defies any classification that I have been able to find. The basic structure is a dodecahedron, but the verticies have been replaced with truncated tetrahedrons and the edges have been replaced with hexagonal prisms. It's a 3D structure that is built of 3D structures that are constructed out of identical individual 3D pieces.

What do you think NASA? Kind of looks like it could be a mars lander.

Below is a picture of our cat Simon hiding behind a Dodecahydroid in our family room.

#
FACETS: How they are made

FACETS begin their life as a piece of maple that is planed, milled, cut, tumbled, pinched, drilled, spun, tilted, redrilled, clamped, and shot with a magnet gun. I have been discussing the manufacturing process for the production of FACETS with Davis Edson of Edson Woodworking in Chicago. (Edson-woodworking.com) Davis has designed and built custom machines for the processing of wooden products and the precision insertion of magnets into pieces of wood. Davis is the current manufacturer for the Drop Catch (DROPANDCATCH.com) which originated as a kickstarter campaign. Based on the intricacy of this particular application (the machine will have to be dedicated solely to the production of FACETS), Davis estimates that it will take about two months for the design and construction (and the elimination of bugs) of the custom FACETS machine. This is the primary reason for the projected delivery date for FACETS. There should not be any difficulty with the procurement of the materials needed to make the FACETS (maple from Canada and magnets from China), but there may be an unexpected glitch in the creation of the custom machine to make them. I do not want to rush the process. However, like so many other start-up projects, FACETS were born in my garage and I want to keep the manufacturing of FACETS in the United States and in the hands of someone like Davis Edson, a woodworker who takes pride in the quality workmanship of the products emerging from his shop. Once it is up and running, Davis estimates that the custom machine will be able to produce about 300 FACETS per hour.

# Budget, Schedule, and all that stuff

The full funding target for this campaign is $12,500 USD. This is the amount that will be needed to build the custom FACETS machine, produce the FACETS and get them boxed and shipped to awaiting FACETS fans.

**Budget** (the proposed operating budget for FACETS is as follows):

- Fees (10%) $ 1,250.00
- Materials (maple and magnets) 3,250.00
- Fulfilment (box and ship) 1,750.00
- Design & construction of custom machine 5,000.00
- Contingency (10%) 1,250.00
- Total Operating Budget $12,500.00

**Schedule**

FACETS will be launched as a 30 day campaign to obtain the necessary pledges for the projected operating budget. Upon full funding, the time required to design and build the custom FACETS machine is estimated to be about two months. Once the machine is up and running, it will take about a week (40 hours of machine run time turning out 300 FACETS per hour) to produce the 12,000 FACETS that will be needed for this campaign. I have allotted an additional 30 days for the boxing and shipping of the sets of FACETS after they are produced. On this schedule it will take about 4 months from the launch of this campaign till the FACETS will be delivered to all my awesome backers. Each stage of this schedule will be squeezed as much as possible to accelerate the delivery of FACETS, but the schedule has been set to minimize the number of explanations that I may have to provide if the production and delivery of FACETS takes longer than expected.

# FACETS: The future

In addition to the original Icosa-FACETS and the HexTetra FACETS of the current campaign, I have prototypes for many different models of FACETS based on the geometries of the different Archimedean solids. The HexTetra FACETS are the simplest to make and extremely flexible in the types of geometric constructions that can be built. If this campaign can be successfully launched and funded then HexTetra FACETS will be followed by Diamond FACETS which are based on the geometry of the rhombic dodecahedron. Diamond FACETS create hexagonal honeycomb structures simultaneously in four separate planes all of which are tilted at the same angle with respect to each of the others (like the faces of a tetrahedron). Very cool.

As a final example, below are a couple of pictures of Rhombo, the FACETS mascot. Rhombo is constructed with rhombic-FACETS which, like Diamond FACETS, are based on the geometry of the rhombic dodecahedron.

### Risks and challenges

The primary challenge to the fulfillment of this project is the design and construction of the custom machine that will tilt, roll, drill and shoot magnets into the FACETS. I have been working with Davis Edson of Edson Woodworking in Chicago for the design and construction of the custom FACETS machine. Davis has considerable experience with the design and construction of automated machines for the production of wooden items similar to FACETS. Davis is the current manufacturer of the Drop Catch which originated as a kickstarter campaign. Although there will be challenges to the fulfillment of this campaign, I have taken the steps that I can to minimize the challenges and difficulties that may arise.

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- (30 days)